Forgoing the carrot-and-stick approach, the City Council is moving to outlaw the sale of rabbits, because the cuddly creatures are multiplying like, well, rabbits.

The council’s Elmer Fudd edict wouldn’t force owners to give up bunnies already in their homes.

But a bill, which had a second public hearing Monday, would make it illegal for pet shops to “display, offer for sale, deliver, barter, auction, give away, transfer or sell” the little critters.

“Rabbits are the third most commonly surrendered animal in city shelters following dogs and cats,” said Christine Mott, who heads the city Bar Association’s Committee on Animal Law.

“They’re frequently dumped in city parks and brought to city shelters. There’s simply not enough room.”

The bunny ban is part of a broader bill that would prohibit pet shops from buying dogs from “puppy mills,” require more dogs to be licensed and give the city stricter enforcement powers over pet stores.

The portion on rabbits was added two weeks ago, said Councilwoman Liz Crowley (D-Queens).

“During holiday times — especially Easter — they’re purchased and often they’re purchased in pairs,” she said after a meeting of the council’s Health Committee.

“That’s why they reproduce so much.”

San Francisco, Los Angeles and Chicago have all banned pet stores from selling rabbits. Petco stopped selling them in 2008.

Unlike dogs and cats, rabbits are more difficult to spay and neuter. When they’re young, it’s hard to determine their gender, which means pet-shop clerks often unwittingly sell customers a boy and girl instead of a same-sex pair.

“That pair turns into 40 bunnies in six months,” Mott said.

Owners are then faced with a daunting choice — keep the growing brood, or turn some of them loose, either at a shelter or in the urban wild.

Their increased popularity has led to the number of unwanted rabbits nearly doubling in city-funded Animal Care and Control shelters — from 216 in 2011 to 399 last year, Crowley said.

Risa Weinstock, the agency’s executive director, noted that city shelters are “at maximum capacity for rabbits.”

And that doesn’t even begin to count the hundreds, if not thousands, released into parks.

“Most of these rabbits are not rescued,” said Natalie Reeves, founder of Big Apple Bunnies. “Most of them get eviscerated by dogs, cats, raccoons, hawks and killed by parasites before they can be rescued.”

Not everyone is in favor of the ban, though.

The Petland Discount shop on Nassau Street in lower Manhattan sells between four and eight rabbits a day, a clerk said.